The ideal interest rate for the US economy in current conditions would be minus 5 per cent, according to internal analysis prepared for the Federal Reserve’s last policy meeting.

The analysis was based on a so-called Taylor-rule approach that estimates an appropriate interest rate based on unemployment and inflation.

A central bank cannot cut interest rates below zero. However, the staff research suggests the Fed should maintain unconventional policies that provide stimulus roughly equivalent to an interest rate of minus 5 per cent.

Fed staff separately estimated what size and type of unconventional operations, including asset purchases, might provide this level of stimulus. They suggested that the Fed should expand its asset purchases by even more than the $1,150bn (€885bn, £788bn) increase policymakers authorised at the last meeting, which included $300bn of Treasury purchases.

The assessment that the US central bank needs to provide stimulus equivalent to a substantially negative interest rate is unlikely to have changed ahead of this week’s policy meeting.

The Fed is not likely to embark on any substantial new programmes at this meeting, in large part because it will not have downgraded its economic forecasts since the last meeting. Indeed, Fed officials may see the risks to the economy as a little more balanced than they were in March, though policymakers probably still see these risks as overall weighted to the downside.

This could set the stage for a more detailed discussion of the framework that will ultimately govern the Fed’s exit strategy.

There is, though, a small but intriguing possibility that the Fed could follow the Bank of Canada in setting out an explicit timeframe over which it expects to keep short-term rates at virtually zero.

While this novel strategy is likely to at least provoke debate within the US central bank, which has shown itself willing to adopt measures first deployed elsewhere, many policymakers would probably be wary of adopting the Canadian approach, following their own unsatisfactory experience in providing guidance on interest rates after the dotcom bubble burst.

Others may feel the Canadian approach would be ineffective as it may not be seen as credibly binding the central bank’s future decisions.

Still, many Fed officials expect they may well keep rates near zero for another 18 months to two years and some might see value in making this more explicit.

Ben Bernanke, chairman, sees the massive expansion of bank reserves caused by the Fed’s unconventional operations as already providing a way to assure the market that the Fed will not be in a position to raise rates for quite some time to come.

The last meeting saw the Fed buy long-term treasuries for the first time in decades. The large initial impact of the move on markets is no longer visible, but officials think the policy was reasonably successful.

Previous staff analysis suggested the $300bn purchase would reduce the yield on 10-year treasuries by 25-35 basis points, and officials think the rate today is about this much lower than it would have been if they had not started buying.

Further purchases are possible, particularly if the Fed again downgrades its economic forecasts. The staff analysis comparing unconventional operations to interest rate cuts suggests more might be needed anyway.

However, policymakers are likely to watch how financial conditions respond to the already-authorised interventions before deciding whether to step up much further.